Method and apparatus of multi-coil MR imaging with hybrid space calibration

ABSTRACT

The present invention provides a system and method for parallel imaging that performs auto-calibrating reconstructions with a 2D (for 2D imaging) or 3D kernel (for 3D imaging) that exploits the computational efficiencies available when operating in certain data “domains” or “spaces”. The reconstruction process of multi-coil data is separated into a “training phase” and an “application phase” in which reconstruction weights are applied to acquired data to synthesize (replace) missing data. The choice of data space, i.e., k-space, hybrid space, or image space, in which each step occurs is independently optimized to reduce total reconstruction time for a given imaging application. As such, the invention retains the image quality benefits of using a 2D k-space kernel without the computational burden of applying a 2D k-space convolution kernel.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of and claims priority to U.S.Ser. No. 11/867,186 filed Oct. 4, 2007, which is a continuation of andclaims priority to U.S. Pat. No. 7,282,917 filed Mar. 30, 2006, thedisclosures of which are incorporated herein by reference.

DISCLOSURE OF PARTIES TO JOINT RESEARCH AGREEMENT

This invention was made with Government support under contract EB002711awarded by the National Institutes of Health. The Government has certainrights in this invention.

BACKGROUND OF THE INVENTION

The present invention relates generally to magnetic resonance (MR)imaging and, more particularly, to a flexible approach for sampling andreconstructing an image of an imaging volume with multiple receivercoils to accelerate data acquisition.

When a substance such as human tissue is subjected to a uniform magneticfield (polarizing field B₀), the individual magnetic moments of thespins in the tissue attempt to align with this polarizing field, butprecess about it in random order at their characteristic Larmorfrequency. If the substance, or tissue, is subjected to a magnetic field(excitation field B₁) which is in the x-y plane and which is near theLarmor frequency, the net aligned moment, or “longitudinalmagnetization”, M_(Z), may be rotated, or “tipped”, into the x-y planeto produce a net transverse magnetic moment M_(t). A signal is emittedby the excited spins after the excitation signal B₁ is terminated andthis signal may be received and processed to form an image.

When utilizing these signals to produce images, magnetic field gradients(G_(x), G_(y), and G_(z)) are employed. Typically, the region to beimaged is scanned by a sequence of measurement cycles in which thesegradients vary according to the particular localization method beingused. The resulting set of received NMR signals are digitized andprocessed to reconstruct the image using one of many well knownreconstruction techniques.

One technique that has been developed to accelerate MR data acquisitionis commonly referred to as “parallel imaging” or “partial parallelimaging”. In parallel imaging, multiple receive coils acquire data froma region or volume of interest. Thus, parallel imaging is used toaccelerate data acquisition in one or more dimensions by exploiting thespatial dependence of phased array coil sensitivity. Parallel imaginghas been shown to be successful in reducing scan time, but also reducingimage blurring and geometric distortions. Moreover, parallel imaging canbe used to improve spatial or temporal resolution as well as increasedvolumetric coverage.

There are several types of parallel imaging reconstruction methods thathave been developed to generate the final, unaliased image fromaccelerated data. These methods can generally be divided into twocategories based on how they treat the reconstruction problem: 1)SENSE-based techniques (Sensitivity Encoding) estimate coil sensitivityprofiles from low-resolution calibration images, which can then be usedto unwrap aliased pixels in image space using a direct inversionalgorithm; and 2) GRAPPA-based techniques (Generalized Auto-calibratingPartially Parallel Acquisition) calculate reconstruction weightsnecessary to synthesize unacquired data directly from acquired data ink-space using an algorithm that does not require coil sensitivityestimates. The reconstruction weights for GRAPPA are calculated from asmall amount of fully sampled calibration data that is typicallyembedded within the scan (“auto-calibration”), but can also be acquiredbefore or after the scan. While both SENSE- and GRAPPA-based approacheshave been successful, in practice, GRAPPA-based techniques have beenshown to be preferred when accurate coil sensitivity estimates cannot beobtained, for example, in reduced FOV applications.

One known GRAPPA technique operates entirely in k-space and uses onlyone-dimensional (1D) convolution kernels. A single set of 1D convolutionkernel weights are determined in k-space and subsequently applied ink-space to reconstruct a full k-space data set for each coil. Eachk-space data set is then Fourier transformed into a single image suchthat there is an image per coil. The coil images are combined, e.g.,using sum-of-squares, to create a final image. This concept ofreconstructing separate k-space data sets for each component coil isprecisely what sets GRAPPA apart from its predecessor, VD-AUTO-SMASH.The combination of component coil magnitude images avoids any inter-coilphase errors and the weight generation on a per coil basis makes GRAPPAno longer require that the sensitivity profiles from the involved coilsform spatial harmonics, such as needed for SMASH-based techniques.

In the GRAPPA method, the GRAPPA weights, a.k.a. 1D GRAPPA kernel, areestimated and applied only on neighboring data along the direction ofacceleration (k_(y)). This is not ideal for most coil configurations,since the sensitivity profiles vary not only in the phase-encodingdirection (direction of acceleration) but also in the frequency-encodingdirection, which is orthogonal to the acceleration direction. As such,it has been suggested that the accuracy of GRAPPA-based techniques canbe improved by using a two-dimensional (2D) rather than a 1D k-spacekernel. Moreover, it is believed that the 2D GRAPPA kernel improves theconditioning of the system matrix and therefore reduces reconstructionnoise and residual errors. However, this accuracy comes at the expenseof an increase in reconstruction time due to the computationallyintensive 2D k-space convolution step.

It would therefore be desirable to have a parallel imaging techniquethat maintains the advantages of parallel imaging, (e.g., reduced scantime), is sufficiently flexible to account for various coilconfigurations such that variations in sensitivity profiles areconsidered, and provides significantly reduced reconstruction times.

BRIEF DESCRIPTION OF THE INVENTION

The present invention provides a system and method for parallel imagingthat overcomes the aforementioned drawbacks. The invention includes aparallel imaging technique that performs reconstructions with a 2Dconvolution kernel that exploits the computational efficienciesavailable when operating in certain data “domains” or “spaces”. Thus,the present invention is not limited to “k-space” such as GRAPPA-basedtechniques or limited to “image space” such as conventional SENSE-basedtechniques. In this regard, the invention separates the reconstructionprocess of multi-coil data into a “training phase” and an “applicationphase” in which reconstruction weights are applied to acquired data tosynthesize (replace) missing data. The choice of data space, i.e.,k-space, hybrid space, or image space, in which each step occurs isindependently optimized to reduce total reconstruction time for a givenimaging application. As such, the invention retains the image qualitybenefits of using a 2D k-space kernel without the computational burdenof applying a 2D k-space convolution kernel.

An MR system comprises a plurality of RF receiver coils includes acomputer programmed to determine a scan parameter to be optimized. Thecomputer is further programmed to access a plurality of reduced MR datasets acquired with the plurality of RF receiver coils. The plurality ofreduced MR data sets may include both undersampled MR data and fullysampled MR calibration data. During a training phase, the computer isprogrammed to calculate reconstruction convolution kernel weights fromthe plurality of MR data sets. During an application phase, the computeris programmed to apply the reconstruction weights to the plurality ofreduced MR data sets to form a plurality of complete MR data sets. Thecomputer can automatically determine from which of k-space, hybridspace, or image space that the reconstruction weights are to bedetermined and automatically determine in which of k-space, hybridspace, or image space to synthesize the plurality of complete MR datasets based on the scan parameter to be optimized.

The invention may be embodied in a computer readable storage mediumhaving a computer program for acquiring and reconstructing MR imagesacquired from a plurality of RF receiver coils. The computer programrepresents instructions that when executed by a computer cause thecomputer to access a plurality of reduced k-space data sets acquiredwith the plurality of RF receiver coils, with the reduced data setsincluding both undersampled and fully sampled data. Each k-space dataset includes MR data encoded in a phase encoded as well as a frequencyencoded direction. The computer is further caused to determinereconstruction kernel weights from the reduced k-space data sets andthen Fourier transform the kernel weights along the frequency encodedimension. The computer is further programmed or caused to Fouriertransform the reduced k-space data sets in the one dimension as well.The transformed kernel weights are then applied to the transformedk-space data sets to synthesize a complete hybrid space for each RFreceiver coil. The computer then reconstructs an image from each hybridspace.

A method of parallel imaging is also disclosed and includes the step ofacquiring a reduced k-space data set from each of the plurality ofreceiver coils, where the k-space data sets may include both imaginglines and calibration data lines. The method continues with the step ofdetermining reconstruction kernel weights from the reduced k-space datasets and transforming, in one dimension, the kernel weights and thek-space data sets to hybrid space. The transformed kernel weights arethen applied to the hybrid space data sets to synthesize a plurality ofcomplete hybrid space data sets. A respective image from each of thecomplete hybrid space data sets is then reconstructed.

A method of MR imaging is disclosed as including the steps of estimatinga 2D k-space kernel from reduced k-space data sets acquired from aplurality of RF receiver coils, applying the 2D k-space kernel as a 1Dconvolution in hybrid space, and reconstructing a plurality of coilimages from a plurality of hybrid space data sets synthesized by the 1Dconvolution.

In another method of MR imaging, a reduced k-space data sets from aplurality of RF coils is transformed into hybrid space. The methodfurther comprises the steps of estimating a 1D kernel in hybrid space byconstraining the kernel coefficients to vary smoothly along thefrequency encode dimension, applying the 1D hybrid space kernel aseither a 1D convolution in hybrid space (applied along the phase encodedirection for each spatial coordinate along the frequency encodedimension) or a point-by-point multiplication in image space, andreconstructing a plurality of coil images from a plurality of hybridspace data sets or image space data sets synthesized by the applicationof the hybrid space kernel.

Therefore, in accordance with one aspect of the invention, an MR systemcomprises a plurality of RF receiver coils and a computer programmed todetermine a scan parameter to be optimized and access a plurality of MRdata sets acquired with the plurality of RF receiver coils. The computeris further programmed to determine calibration weights from theplurality of MR data sets, automatically determine from which ofk-space, hybrid space, or image space the calibration weights are to bedetermined, and automatically determine in which of k-space, hybridspace, or image space to supplement the plurality of MR data sets withthe calibration weights based on the scan parameter to be optimized.

In accordance with another aspect, the present invention is directed toa computer readable storage medium having a computer program foracquiring and reconstructing MR images from a plurality of RF receivercoils and representing instructions that when executed by a computercause the computer to obtain calibration k-space data lines from aplurality of k-space data sets acquired with the plurality of RFreceiver coils. Each data set includes MR data encoded in a phaseencoded and a frequency encoded direction. The computer is furthercaused to determine calibration weights from the calibration k-spacedata lines and Fourier Transform the calibration weights in onedimension. The computer then Fourier Transforms the k-space data sets inone dimension and applies the transformed calibration weights to thetransformed k-space data sets to synthesize a hybrid space of desiredsize for each RF receiver coil. The computer is also programmed toreconstruct an image from each hybrid space.

According to another aspect of the invention, a method of parallelimaging is disclosed as including the steps of acquiring a k-space dataset from each of a plurality of receiver coils and acquiring a set ofk-space calibration data lines from each of a plurality of receivercoils. The method also includes the steps of determining kernel weightsfrom the calibration data lines in k-space and transforming, inone-dimension, the kernel weights and the k-space data sets to hybridspace. The transformed kernel weights are applied to the hybrid spacedata sets to synthesize a plurality of complete hybrid space data setswhereupon the method continues with reconstructing a respective imagefrom each of the complete hybrid space data sets.

The invention is also embodied in a method of MR imaging that includesthe steps of estimating a 2D k-space kernel from k-space data acquiredfrom a plurality of RF receiver coils and applying the 2D k-space kernelas a 1D convolution in hybrid space. The method continues with the stepof reconstructing a plurality of coil images from a plurality of hybridspace data sets synthesized by the 1D convolution.

In accordance with another aspect, the invention includes a method of MRimaging comprising the steps of acquiring a plurality of k-space datasets from a plurality of RF receiver coils, acquiring a plurality ofcalibration k-space data sets from the plurality of RF receiver coils,performing a 1D Fourier Transform along a frequency encode direction tocreate hybrid space data sets and hybrid space calibration data sets,and estimating coefficients of continuous weight functions that buildunique sets of 1D hybrid space kernel weights for each location in thefrequency encode direction and constrains the 1D hybrid space kernelweights to vary smoothly. The method further includes the steps ofbuilding the continuous weight functions by a set of basis functionssuitable for the coil configuration, applying the 1D hybrid space kernelweights to the hybrid space data sets as a 1D convolution in hybridspace, or a point-by-point multiplication in image space, andreconstructing a plurality of coil images from a plurality of hybridspace data sets or image space data sets.

In yet another aspect of the invention, a MR system has a computerprogrammed to obtain a number of fully sampled calibration k-space datalines from a plurality of 3D MR data sets and determine reconstructionweights from the calibration k-space data lines. The computer is alsoprogrammed to perform a 1D Fourier Transform along k_(x) on thecalibration weights to convert the calibration weights to hybrid spaceand perform a 1D Fourier Transform along k_(x) on the plurality of MRdata sets to convert the MR data sets from k-space to hybrid space. Thecomputer then supplements the plurality of MR data sets in hybrid spacewith hybrid space calibration weights and performs a 2D FourierTransform on the supplemented MR data sets to convert each data set to3D image space.

Various other features and advantages of the present invention will bemade apparent from the following detailed description and the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings illustrate one preferred embodiment presently contemplatedfor carrying out the invention.

In the drawings:

FIG. 1 is a schematic block diagram of an MR imaging system for use withthe present invention.

FIG. 2 is a schematic of a coil array usable with the MR imaging systemshown in FIG. 1.

FIG. 3 is a process map illustrating a preferred reconstruction flow inaccordance with one aspect of the invention.

FIG. 4 is a schematic showing that the present invention obtains a moreaccurate fit when the reconstruction location is near the calibrationregion.

FIG. 5 is a schematic illustrating that the present invention candetermine calibration weights from non-zero-padded data.

FIG. 6 is a schematic illustrating the variability provided by thepresent invention.

FIG. 7 is a process map illustrating the reconstruction flow inaccordance with one aspect of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention is directed to a parallel imaging technique thatis applicable to k-space, hybrid space, or image space data. K-space iswell-known in the art of MR imaging as a matrix that functions as, or isequivalent to, a “frequency domain” repository for positive and negativespatial frequency values that are encoded as complex numbers, e.g.,a+bi, i=sqrt(−1). That is, the k-space matrix is generally recognized asthe repository for spatial frequency signals acquired during evolutionand decay of an MR echo. The k-space matrix is typically filled withfrequency encoded data in the k_(x) direction by a frequency encodegradient and in the k_(y) direction by a phase encode gradient, and canalso include phase encoded data in the k_(z) direction by a second phaseencode gradient. Data acquired from the echo is deposited in the k-spacematrix in a row, specifically determined by the frequency and phaseencode gradient strengths applied during MR signal evolution. K-space isgenerally filled one row at a time in a Cartesian manner. After all thek-space has been acquired, the elements of the k-space matrix containpositionally-dependent phase change variations along the k_(x)(frequency encode) and k_(y) (phase encode) direction. A 2D inverseFourier transform decodes the frequency domain information. The 2DFourier transform is a two step process. First, a row-by-row 1D Fouriertransform converts each row of k-space data. After the row-by-rowFourier transform, a column-by-column 1D Fourier transform is performed.Collectively, the pair of 1D Fourier transforms converts the k-spacedata from the frequency domain (k-space data) to the spatial domain(image space data). An image is then reconstructed from the image matrixillustrating spatial and contrast characteristics of the object imaged.

“Hybrid space” refers to the intermediate matrix that results in theperformance of one of the 1D Fourier transforms that comprise the 2DFourier transform that converts k-space to image space. In other words,in 2D Fourier imaging, one Fourier transform is performed in thefrequency encoding direction and another Fourier transform is performedin the phase encoding direction. The matrix after the first 1D Fouriertransform is considered a “hybrid space”. That is, the data is no longer“untransformed” and therefore not considered k-space; however, the data,as a whole, is not yet in the spatial domain and, thus, not in “imagespace”.

Referring to FIG. 1, the major components of a preferred magneticresonance imaging (MRI) system 10 incorporating the present inventionare shown. The operation of the system is controlled from an operatorconsole 12, which includes a keyboard or other input device 13, acontrol panel 14, and a display screen 16. The console 12 communicatesthrough a link 18 with a separate computer system 20 that enables anoperator to control the production and display of images on the displayscreen 16. The computer system 20 includes a number of modules, whichcommunicate with each other through a backplane 20 a. These include animage processor module 22, a CPU module 24 and a memory module 26, knownin the art as a frame buffer for storing image data arrays. The computersystem 20 is linked to disk storage 28 and tape drive 30 for storage ofimage data and programs, and communicates with a separate system control32 through a high speed serial link 34. The input device 13 can includea mouse, joystick, keyboard, track ball, touch activated screen, lightwand, voice control, or any similar or equivalent input device, and maybe used for interactive geometry prescription.

The system control 32 includes a set of modules connected together by abackplane 32 a. These include a CPU module 36 and a pulse generatormodule 38 which connects to the operator console 12 through a seriallink 40. It is through link 40 that the system control 32 receivescommands from the operator to indicate the scan sequence that is to beperformed. The pulse generator module 38 operates the system componentsto carry out the desired scan sequence and produces data which indicatesthe timing, strength and shape of the RF pulses produced, and the timingand length of the data acquisition window. The pulse generator module 38connects to a set of gradient amplifiers 42, to indicate the timing andshape of the gradient pulses that are produced during the scan. Thepulse generator module 38 can also receive patient data from aphysiological acquisition controller 44 that receives signals from anumber of different sensors connected to the patient, such as ECGsignals from electrodes attached to the patient. And finally, the pulsegenerator module 38 connects to a scan room interface circuit 46 whichreceives signals from various sensors associated with the condition ofthe patient and the magnet system. It is also through the scan roominterface circuit 46 that a patient positioning system 48 receivescommands to move the patient to the desired position for the scan.

The gradient waveforms produced by the pulse generator module 38 areapplied to the gradient amplifier system 42 having Gx, Gy, and Gzamplifiers. Each gradient amplifier excites a corresponding physicalgradient coil in a gradient coil assembly generally designated 50 toproduce the magnetic field gradients used for spatially encodingacquired signals. The gradient coil assembly 50 forms part of a magnetassembly 52 which includes a polarizing magnet 54 and a whole-body RFcoil 56. A transceiver module 58 in the system control 32 producespulses which are amplified by an RF amplifier 60 and coupled to the RFcoil 56 by a transmit/receive switch 62. The resulting signals emittedby the excited nuclei in the patient may be sensed by the same RF coil56 and coupled through the transmit/receive switch 62 to a preamplifier64. The amplified MR signals are demodulated, filtered, and digitized inthe receiver section of the transceiver 58. The transmit/receive switch62 is controlled by a signal from the pulse generator module 38 toelectrically connect the RF amplifier 60 to the coil 56 during thetransmit mode and to connect the preamplifier 64 to the coil 56 duringthe receive mode. The transmit/receive switch 62 can also enable aseparate RF coil (for example, a surface coil) to be used in eithertransmit or receive mode.

The MR signals picked up by the RF coil 56 are digitized by thetransceiver module 58 and transferred to a memory module 66 in thesystem control 32. A scan is complete when an array of raw k-space datahas been acquired in the memory module 66. This raw k-space data isrearranged into separate k-space data arrays for each image and eachcomponent coil to be reconstructed, and each of these is input to acentral processing unit 68 which operates to Fourier transform the datainto an array of image data. This image data is conveyed through theethernet link 34 to the computer system 20 where it is stored in memory,such as disk storage 28. In response to commands received from theoperator console 12, this image data may be archived in long termstorage, such as on the tape or disk drive 30, or it may be furtherprocessed by the image processor 22 and conveyed to the operator console12 and presented on the display 16.

The MR system described in FIG. 1 may also be equipped with a receivecoil array that picks up the MR signals. Such coil arrays are well-knownin the art and include whole body arrays as well as partial body arrays,such as head coil arrays, cardiac coil arrays, and spine coil arrays. Aswill be described, the invention includes a parallel imaging methodwherein a region or volume of interest is sampled with an array of RFreceive coils. In this regard, the invention is not limited to aparticular coil array type or orientation.

Referring now to FIG. 2, a schematic representation of a conventionaltorso RF coil array 70 is illustrated. The torso RF coil array 70 is asurface coil used to acquire imaging data for a field-of-view (FOV) andincludes eight separate coil elements 72-79. Each coil element samplesthe FOV by detecting changes in excited nuclei in the FOV and transmitssignals indicative of that which is detected to separate dataacquisition channels 80-87, respectively. The data from each channel isthen used to reconstruct a “coil” image 88-95 whereupon the respectivecoil images are combined into a composite image 96 using one of a numberof known summation techniques, e.g., sum of squares. One skilled in theart will appreciate that the coil array illustrated in FIG. 2 isexemplary and that the invention is not limited to parallel acquisitionusing such a coil array.

As is known in the art of parallel imaging, the sensitivity of each coilelement to the FOV can be exploited to accelerate the data acquisitionprocess. The image data of each coil are multiplied by the coilsensitivity inherent to each coil element. The corresponding k-spacedata are convolved with the Fourier Transform of the spatial coilsensitivity distribution. The spatial coil sensitivity variation imposedby the individual receive coils provides additional spatial encodingfunctionality complementary to regular gradient encoding that is thebasis of all parallel imaging methods. In 2D imaging, that sensitivityis exploited to reduce the number of phase encoding steps in onedimension or direction. In 3D imaging, that sensitivity can be exploitedto reduce the number of phase encoding steps in up to two dimensions ordirections.

The present invention is directed to a parallel imaging technique thatincludes a “training phase” and an “application phase”, similar to thatin GRAPPA-based approaches. However, unlike GRAPPA-based approaches, thepresent invention is not limited to performing both the training andapplication phases in the k-space domain. In this regard, the presentinvention is not limited to any one data space but rather has theflexibility to be performed in k-space, hybrid space, image space, orcombinations thereof depending upon the particulars of the MR study. Itis preferred that the “training phase” take place in either k-space orhybrid space and that the “application phase” take place in eitherhybrid space or image space. Doing so still retains the image qualitybenefits of a 2D k-space kernel. Specifically, as will be set forthbelow, reconstruction with the present invention can take the form of a2D convolution in k-space, a 1D convolution in hybrid space, or apoint-by-point multiplication in image space.

In one embodiment of the invention, the training phase and theapplication phase are performed in the same domain. For example, theentire reconstruction process is performed in hybrid space. Theimplementation is shown in FIG. 3 for exemplary purposes as being for acoil array comprising two coils. In the illustrated implementation, twoseparate k-space data sets 97, 98 are acquired. Each k-space data setcomprises data sampled from a reduced FOV by a respective coil.Moreover, each k-space data set includes imaging data lines 99, 100 andcalibration data lines 101, 102, respectively. As shown, each k-spaceset is undersampled in the phase encoding direction. That is, a reducednumber of phase encoding steps are undertaken so as to reduce scan time.As will be described, the missing phase encoding lines will besynthesized mathematically from the acquired data. Those skilled in artwill recognize that the calibration data can also be acquired separatelyrather than embedded within the scan, so that full acceleration can beaccomplished for the parallel imaging scan.

The k-space data sets are Fourier transformed in the one dimension togenerate hybrid space data sets 103, 104. Preferably, the 1D Fouriertransformations are in the frequency encoding direction. Thereconstruction weights 106 are then estimated directly from hybrid spacedata.

Then, in the application phase, missing data in the hybrid spaces 103,104, i.e., the undersampled phase encoding locations, is synthesizedefficiently from the acquired imaging and calibration data in hybridspace by single matrix-vector multiplication so as to yield completehybrid spaces 108, 110. In other words, the phase encoding locationsthat were not sampled are filled from the single matrix-vectormultiplication. The hybrid spaces 108, 110 are reconstructed torespective coil images 112, 114, by application of a 1D Fouriertransformation in the phase encoding direction. This results in a “coil”image for each coil of the phase coil array. The individual coil imagesare then combined to yield a single composite image 118 of the FOV.

The reconstruction process illustrated in FIG. 3, as mentioned above,performs the training and application phases in the same domain—thehybrid domain. In this regard, the kernel weights are applied to MR datathat is in the spatial domain in the frequency encoding direction and inthe k-space domain in the phase encoding direction. In this embodiment,a 1D Fourier transform is performed along the frequency encodingdirection to convert the sampled k-space data to hybrid space. Thecalculation of unique 1D convolution kernel weights at each frequencyencoded position in hybrid space, however, can be a heavilyunder-determined problem that can result in noisy reconstructed images.However, under the assumption that the coil sensitivity varies smoothlyin the spatial domain, the weights along the frequency encodingdirection can be related to one another with smoothly varying,continuous weight functions represented by a set of basis functions,e.g. a cosine or B-spline basis set. Thus, the reconstruction problembecomes well conditioned. Here, weight functions can be found thatreduce fitting errors and lead to improved image quality. The choice ofthe basis set of functions can vary and may depend on various factors,such as coil configuration. In the training phase, the coefficients ofthe basis functions that build the weight functions are estimated fromthe fully sampled calibration data in hybrid space, which amounts to asingle matrix inversion problem. Then, in the application phase, missingdata is synthesized efficiently from the acquired data in hybrid spaceby a single matrix-vector multiplication.

In another embodiment, the training phase of the reconstruction processis performed in one domain and the application phase of thereconstruction process is performed in another domain. For example, the2D k-space kernel weights can be first determined in k-space, thentransformed into either hybrid space weights or image space weights tobe applied to imaging data that has been similarly transformed into thatspace. The implementation of determining kernel weights in k-space andtransforming them into hybrid space is shown in FIG. 7 for exemplarypurposes as being for a coil array comprising two coils.

In the illustrated implementation, two separate k-space data sets 138,140 are acquired. Each k-space data set comprises data sampled from anFOV by a respective coil. Moreover, each k-space data set includesimaging data lines 142, 144 and calibration data lines 146, 148,respectively. As shown, each k-space set is undersampled in the phaseencoding direction. That is, a reduced number of phase encoding stepsare undertaken so as to reduce scan time. As will be described, theundersampled phase encoding steps will be accounted for mathematicallyfrom the acquired data.

The data embodied in the calibration data lines 146, 148 is used toderive k-space weights 150. Those weights are then Fourier transformedin one dimension to form a set of hybrid weights 152. The k-space datasets are Fourier transformed in the one dimension to generate hybridspace data sets 154, 156. Preferably, the 1D Fourier transformations arein the frequency encoding direction. Then, in the application phase,missing data in the hybrid spaces 154, 156, i.e., the undersampled phaseencoding locations, is synthesized efficiently from the acquired imagingand calibration data in hybrid space so as to yield complete hybridspaces 158, 160. The hybrid spaces 158, 160 are reconstructed torespective coil images 162, 164, by application of a 1D Fouriertransformation in the phase encoding direction. This results in a “coil”image for each coil of the phase coil array. The individual coil imagesare then combined to yield a single composite image 166 of the FOV.

Because calculating the 2D k-space kernel weights can be performed veryefficiently in k-space, whereas applying the weights can be performedmost efficiently in image space or hybrid space, such a multi-domainapproach optimizes net computational efficiency compared to approachesthat operate entirely in k-space. This is because the 2D convolution ink-space is replaced by 1D convolutions or multiplications with thetransformed kernel in the hybrid or spatial domain, respectively.

It is also contemplated that the training phase and application phasescan be performed entirely in image space, although the calculation ofweights in image space is not as efficient as in k-space or hybridspace. It should be noted that this image-based approach differs fromconventional SENSE-based approaches because unlike SENSE, the presentinvention does not require sensitivity estimation and; furthermore,performs a fitting algorithm rather than a direct matrix inversion toreconstruct images.

The multi-domain approach of determining weights in k-space and applyingthem in image space is particularly preferred for time-seriesacquisitions. In such a study, the calibration data is acquired in onlythe first acquisition. The determined weights are then applied to thefirst and subsequent acquisitions. In this regard, the subsequenttime-series acquisitions are not burdened by the acquisition ofcalibration data. The calibration data and reconstruction weights can bereacquired and updated periodically throughout the time series. Adrawback to performing the application phase in image space is that itrequires a uniform k-space sampling density, a condition that can onlybe achieved with regularly undersampled data from which theauto-calibration lines have been removed, resulting in reduced SNR andthe inability to achieve flexible sampling patterns. Furthermore, theFourier transformation of the kernel weights from k-space to image spaceis not negligible. However, in the case of time-series imaging where theauto-calibration data is acquired just once at the beginning of the scanand then used to reconstruct a series of time-resolved images at thesame location, performing the application phase in image space becomescomputationally efficient.

Performing the application phase in hybrid space retains the flexibilityof non-uniform sampling patterns and does not require the removal ofauto-calibration lines. Furthermore, it allows tailoring the fittingpatterns to the particular sampling pattern to include all availableneighboring data, thus improving the accuracy of the fit. This is incontrast to GRAPPA which uses the same kernel weights and fittingpattern to estimate the data for all reconstruction locations. Incontrast to GRAPPA, in hybrid space and k-space the present inventionvaries the fitting pattern to include the acquired data locations in alocal neighborhood. As shown in FIG. 4, when the reconstruction location120 is near the calibration region 122, the present invention takesadvantage of the increase in locally acquired data to obtain a moreaccurate fit. In addition, the present method finds unique weights atthe edges of k-space based solely on the acquired data points, asillustrated in FIG. 5. As illustrated in FIG. 5, the weights arepreferably found without zero-padding of k-space or hybrid space.

As referenced above, the present invention is directed to areconstruction process for parallel imaging that is flexible to accountfor various scan goals or parameters, such as computation time, coilconfiguration, etc. As such, the present invention can be summarized bythe flow map illustrated in FIG. 6. As shown thereat, kernel weights canbe derived in k-space and either 1D Fourier transformed or 2D Fouriertransformed to hybrid space weights 126 or image space weights 128,respectively. If the weights are converted to hybrid weights 126, thoseweights can then be applied in hybrid space to remove aliasing 130. Onthe other hand, the image space weights are applied in image space toremove aliasing 132. As also shown in FIG. 6, the kernel weights can bedetermined in hybrid space 134 and applied directly in hybrid space 130to remove aliasing similar to that described in FIG. 3. Each of theabove described paths is preferred from determining and applying theweights in k-space 124, 136. Further, it is believed the mostcomputationally efficient approach for most applications, shown withshading, is to determine the weights from k-space 124, convert thoseweights to hybrid space 126, and then apply the weights in hybrid space130, similar to that described in FIG. 7.

The present invention provides an efficient reconstruction of multi-coilMR data with reduced data processing time that is of sufficientflexibility to account for variations in coil sizes, orientations, andother scan parameters. It is believed the advantages of the presentinvention will be particularly realized as array sizes increase. Theinvention is also applicable with 1D accelerated (e.g. for 2D imaging)as well as 2D accelerated (e.g. 3D imaging) applications. It is alsobelieved that the present invention provides a cost savings toconventional approaches by reducing hardware requirements. It is furtherbelieved that the invention provides an image quality improvementrelative to previous k-space domain approaches that did not use allavailable data to reconstruct missing data.

Accordingly, the invention can advantageously perform the training andapplication steps of the reconstruction in data domains other thanexclusively in k-space. Moreover, the invention offers the flexibilityto switch between data domains between reconstruction steps. Forexample, the training phase can be performed in either k-space or hybridspace and then the application phase can be performed in either hybridspace or image space. The flexibility of the invention allows for thereconstruction to be adapted on a per scan basis as the goals of a scansvary. Moreover, this flexibility allows the reconstruction to takeadvantage of the benefits available when working in a particular dataspace at each processing step.

Therefore, an MR system comprises a plurality of RF receiver coils and acomputer programmed to determine a scan parameter to be optimized andaccess a plurality of MR data sets acquired with the plurality of RFreceiver coils. The computer is further programmed to determinecalibration weights from the plurality of MR data sets, automaticallydetermine from which of k-space, hybrid space, or image space thecalibration weights are to be determined, and automatically determine inwhich of k-space, hybrid space, or image space to supplement theplurality of MR data sets with the calibration weights based on the scanparameter to be optimized.

The present invention is also directed to a computer readable storagemedium having a computer program for acquiring and reconstructing MRimages from a plurality of RF receiver coils and representinginstructions that when executed by a computer cause the computer toobtain calibration k-space data lines from a plurality of k-space datasets acquired with the plurality of RF receiver coils. Each data setincludes MR data encoded in a phase encoded and a frequency encodeddirection. The computer is further caused to determine calibrationweights from the calibration k-space data lines and Fourier Transformthe calibration weights in one dimension. The computer then FourierTransforms the k-space data sets in one dimension and applies thetransformed calibration weights to the transformed k-space data sets tosynthesize a hybrid space of desired size for each RF receiver coil. Thecomputer is also programmed to reconstruct an image from each hybridspace.

A method of parallel imaging is also disclosed as including the steps ofacquiring a k-space data set from each of a plurality of receiver coilsand acquiring a set of k-space calibration data lines from each of theplurality of receiver coils. The method also includes the steps ofdetermining kernel weights from the calibration data lines in k-spaceand transforming, in one-dimension, the kernel weights and the k-spacedata set to hybrid space. The transformed kernel weights are applied tothe hybrid space data sets to synthesize a plurality of complete hybridspace data sets whereupon the method continues with reconstructing arespective image from each of the complete hybrid space data sets.

The invention is also embodied in a method of MR imaging that includesthe steps of estimating a 2D k-space kernel from k-space data acquiredfrom a plurality of RF receiver coils and applying the 2D k-space kernelas a 1D convolution in hybrid space. The method continues with the stepof reconstructing a plurality of coil images from a plurality of hybridspace data sets synthesized by the 1D convolution.

The invention further includes a method of MR imaging comprising thesteps of acquiring a plurality of k-space data sets from a plurality ofRF receiver coils, acquiring a plurality of calibration k-space datasets from the plurality of RF receiver coils, performing a 1D FourierTransform along a frequency encode direction to create hybrid space datasets and hybrid space calibration data sets, and estimating coefficientsof continuous weight functions that build unique sets of 1D hybrid spacekernel weights for each location in the frequency encode direction andconstrains the 1D hybrid space kernel weights to vary smoothly. Themethod further includes the steps of building the continuous weightfunctions by a set of basis functions suitable for the coilconfiguration, applying the 1D hybrid space kernel weights to the hybridspace data sets as a 1D convolution in hybrid space, or a point-by-pointmultiplication in image space, and reconstructing a plurality of coilimages from a plurality of hybrid space data sets or image space datasets.

A MR system is also disclosed as having a computer programmed to obtaina number of fully sampled calibration k-space data lines from aplurality of 3D MR data sets and determine reconstruction weights fromthe calibration k-space data lines. The computer is also programmed toperform a 1D Fourier Transform along k_(x) on the calibration weights toconvert the calibration weights to hybrid space and perform a 1D FourierTransform along k_(x) on the plurality of MR data sets to convert the MRdata sets from k-space to hybrid space. The computer then supplementsthe plurality of MR data sets in hybrid space with hybrid spacecalibration weights and performs a 2D Fourier Transform on thesupplemented MR data sets to convert each data set to 3D image space.

The present invention has been described in terms of the preferredembodiment, and it is recognized that equivalents, alternatives, andmodifications, aside from those expressly stated, are possible andwithin the scope of the appending claims.

1. A parallel magnetic resonance (MR) apparatus comprising: a pluralityof receiver coils, each receiver coil configured to acquire a k-spacedata set; and a control processor programmed to: receive a set ofk-space calibration data lines from each of the plurality of receivercoils; determine a set of kernel weights from the calibration data linesin k-space; transform, in one dimension, the set of kernel weights tohybrid space to form hybrid space kernel weights; transform, in onedimension, each k-space data set to form a plurality of hybrid spacedata sets; apply the hybrid space kernel weights to the plurality hybridspace data sets to synthesize MR data for each receiver coil; for eachreceiver coil, combine the synthesized MR data with the acquired k-spacedata set for the receiver coil; and reconstruct an image for eachreceiver coil based on the combination of the synthesized MR data andthe acquired k-space data set for the receiver coil.